Schur stability of polytopes of bivariate polynomials

Necessary and sufficient conditions for Schur stability of polytopes of bivariate polynomials have been established. Based on a simplification, the two-dimensional (2-D) analysis for stability of polytopes of 2-D polynomials is turned into that of polytopes of one-dimensional (1-D) polynomials with complex variable coefficients. We reveal that the uncertain coefficients of the 2-D polytopes possess a linear affine property, and then show that the stability of a polytope of bivariate polynomials can be guaranteed by that of finite edge polynomials of the polytope. An algorithm for the stability test of edge polynomials is provided.